2025/03/12 by Antonopoulos, Lucky K., Lewis, Dominic G., Davis, Jack +2 · 1 citation
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2503.09353
Wigner functions help visualise quantum states and dynamics while supporting quantitative analysis in quantum information. In the discrete setting, many inequivalent constructions coexist for each Hilbert-space dimension. This fragmentation obscures which features are fundamental and which are artefacts of representation. We introduce a stencil-based framework that exhausts all possible d× d discrete Wigner functions for a single d-dimensional quantum system (including a novel one for even d), subsuming known forms. We also give explicit invertible linear maps between definitions within the same d, enabling direct comparison of operational properties and exposing representation dependence.